Two main reasons are usually given for this:

(1) It optimally orients the vehicle in case of an RTLS (Return To Launch Site) abort.

Oriented "heads down", a simple powered pitch around maneuver is needed to return. Oriented "heads up", a more complicated roll plus pitch maneuver would be required.

(2) It decreases structural loading on the wings vs a "heads up" orientation. Heads down, the vehicle pitch is oriented to a slight negative angle of attack (wind flow relative to wings). Wings generate lift -- the higher speed the more lift. A slight negative angle of attack nulls this out thus lowering wing stress.

There are also less important reasons: it helps with comm coverage (antennas are on top of the orbiter), it provides the crew with a better horizon view, etc.

The vehicle is physically capable of flying a "heads up" profile and in fact that helps payload slightly. However because of the RTLS abort and wing loading issues I doubt they'll ever do that.

Why not just build the launch pad pointed the right direction? To save money the shuttle uses the old Saturn V pad. That was oriented south to facilitate alignment of the older guidance platform. However the shuttle flies (or used to fly) different inclinations. ISS is 52 degrees, whereas Hubble is 28 degrees (angle from the equator). Each one would require a different amount of roll so even if the pad was pointed toward the most common ascent inclination, some roll would still be necessary.